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Makhlouf, Abdellatif Ben; Mchiri, Lassaad; Arfaoui, Hassen; Dhahri, Slim; El-Hady, El-Sayed; Cherif, Bahri

Hadamard Itô-Doob stochastic fractional order systems. (English) Zbl 1517.60064

Discrete Contin. Dyn. Syst., Ser. S 16, No. 8, 2060-2074 (2023).
Summary: In this paper, we study the existence and uniqueness of Hadamard Itô-Doob Stochastic Fractional Order Systems (HIDSFOS) using the Picard iteration method. Different from the previous works, our paper presents a new theory using the Hadamard fractional integral. We have proved the convergence of the solution of the averaged HIDSFOS to that of the standard HIDSFOS in the sense of the mean square and also in probability. Some examples are given at the end of this paper to illustrate our theoretical results.

Cited in 2 Documents

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34A08 Fractional ordinary differential equations
34F05 Ordinary differential equations and systems with randomness

Keywords:

stochastic system
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References:

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